Asteroid Orbit Determination Project

In the summer of 2009 I participated in a program called the Summer Science Program (SSP) which really started my interest in computer science. Our main project in this program was to determine the orbit of an asteroid which basically means to find the six orbital elements that uniquely define its orbit: a (semimajor axis), e (eccentricity), i (inclination), Ω (longitude of the ascending node), ω (argument of perihelion), and M_observed (mean anomaly).

The asteroid orbit determination project was used to determine the orbit of a near-earth asteroid, one whose orbit is similar to earth's orbit around the sun. After obtaining measurements for three Through observations and calculations, we are able to find the six orbital elements that uniquely define an asteroid's orbit.

The asteroid orbit determination project consisted of several steps:

1. Choosing an asteroid
2. Observing the asteroid
3. LSPR to determine the equatorial coordinates of the asteroid
4. Orbit Determination to determine the orbital elements that describe the asteroid’s orbit

We first selected an asteroid from the Minor Planet Center's list of near -earth asteroids. There were many factors in determining an adequate asteroid to observe. First of all, it had to be observable from our location and not located on the other side of the earth and had to be bright enough. In the end we chose the asteroid 2000 PJ5 because it met these requirements and also was a fairly quickly moving asteroid which meant we could more easily identify it on captured images.

We used a 14″ Meade LX-200RX reflector and SBIG STL-1301E CCD camera to take images of our asteroid. Over the course of four weeks, we observed on six different occasions using the Meade Telescope. We found the asteroid in all but the first observation and obtained measurable images during four of those. Our first and third images with the asteroid were immediately measurable, while the second image was out of focus due to humidity. We, thus, observed again to attain another measurable image. We determined which spot was our asteroid by comparing multiple images of the same snapshot and looking for a spot that moved, as stars are motionless:

The telescope we used

Once we had the images of our asteroid we needed to determine the equatorial coordinates of our asteroid, or basically its location in the sky. Using The Sky Software, we found the locations of reference stars surrounding our asteroid to determine the location of our asteroid using the Least-Squares Plate-Reduction (LSPR) method that we programmed in VPython.

An example of TheSky software

Upon finding the equatorial coordinates for the three sets of observation data, it was theoretically possible to calculate the classical orbital elements of 2000 PJ5. To do so, we used Gauss’s Method of Orbit Determination, programmed in VPython, which takes the data from three observations to determine the six orbital elements:

1. Eccentricity: Basically the shape of the ellipse, where values close to zero are more elongated while values closer to one are more circular.
2. Semimajor Axis: Half the length of the major axis of the orbit of the asteroid.
3. Inclination: The tilt of the orbit from the reference plane. In this case, the reference plane was the ecliptic plane where the orbits of the planets are located.
4. Longitude of the Ascending Node: The angle the orbit is rotated from the reference plane's vernal point, basically describes where the asteroid “ascends” out from the reference plane.
5. Argument of Periapsis: The orientation of the ellipse, or the angle the orbit is rotated with respect to itself.
6. Mean Anomaly: The locations of the asteroid in a certain time period.

After determining these elements we were able to generate a visualization of the orbit of the asteroid: